Resonant X-ray diffraction study and electronic structure calculations of three Mo-Ru-Si ternary phases

Resonant X-ray diffraction experiments at the Mo K-edge have been performed to study three ternary phases of the Mo-Ru-Si system with compositions Mo58Ru32Si10 (σ-phase, CrFe type), Mo40Ru40Si20 (χ-phase, αMn type) and Mo26Ru45Si29 (β-phase) with the aim of increasing the scattering contrast between Ru and Mo. Multi-pattern Rietveld refinements allowed localizing the metallic elements on the different crystallographic sites of these structures. Chemical disorder was detected in all three investigated phases and the distribution of the elements was analyzed as a function of the atomic coordination and site volume. The two Frank-Kasper phases, σ and χ, are two phases showing the more pronounced atomic mixing with a tendency for Mo to prefer high coordination number (CN) sites while Si is excluded from these sites. The β-phase presents complete ordering of silicon on the sites with the smallest volumes. The total energy calculations, using the Korringa-Kohn-Rostoker method with the coherent potential approximation, were performed for different substitutional configurations of these three phases. The computed negative values of the formation energy support the experimental findings showing that Si prefers the crystallographic sites with the lowest CN. On the contrary, putting Si atoms in high CN crystallographic sites leads to substantial increase of the total energy and positive value of the formation energy. Moreover, several features of the density of states calculated for the most stable models are discussed.